Metal is a material extracted from ore at a smelter, turning the ore into bars of pure metal. (One special metal becomes wafers instead of bars.) It is sometimes combined with other materials to form an alloy metal, which is also measured by the bar. An alloy usually improves on the properties of its components to give more uses or increased value. The metal bars resulting from smelting are used to make items such as weapons, armor, furniture, and crafts at a forge.

Smelting pure ores into the corresponding bars raises the base value from that of stone (3) to that of bars (5). This value is then multiplied against the material multiplier of the metal to give the final value for the bar.

Contents

There are eleven pure metals in Dwarf Fortress (plus a twelfth special metal). Many of these can be mixed together to create alloys of one type or another, of which there are another fourteen. In some cases making alloys will result in an overall increase in value, or the resultant alloy will be more powerful when used to forge weapons or armor, though many alloys result in no overall increase in utility or created wealth. (These increases in value can be compared in the "Difference" column of the below table.)

There are many uses for alloys:

Increased performance for armor or weapons.

Increased value (particularly when a silver-bearing ore is substituted for silver)

Increasing happiness or perceived room value for a dwarf who particularly likes a given alloy.

Decreased fuel consumption if making the alloy directly from ores (e.g. bronze requires only one smelter task to make 8 bars from 2 ores).

The number of bars used to create an alloy always equals the number of bars produced: the number of bars input equals the number of bars of output. However, the number of bars produced from smelting ores is four times greater (X ores in = 4X bars out).

Density is used to determine the different weight of finished objects.

Melting point is used to determine if a material is magma-safe or not: magma is 12000°U.

Material value is what the base value of an object made of this metal is multiplied by to determine its worth.

Value difference indicates the difference between the average value of the required bars of metals vs. the value of the resulting bars of alloy - what went in vs. what comes out, measured per bar. "+0" indicates that the resulting alloy is a perfectly average value of the component metals. Note that substituting tetrahedrite for copper ore always results in a value decrease, while substituting tetrahedrite or galena for silver ore always results in a value increase.

Combat information is used internally by the game to determine the combat properties of weapons and armor made from this metal:

Density: Used in conjunction with other factors - heavier weapons (higher numbers) hit with more force, light weapons tend to have less penetration. Value shown here is g/cm3, which is the raw value divided by 103

Impact yield: Used for blunt-force combat; higher is better. This is the raw value divided by 103 (i.e., kPa).

Impact fracture: Used for blunt-force combat; higher is better. This is the raw value divided by 103 (i.e., kPa).

Impact elasticity: Used for blunt-force combat; lower is better. This is the raw value.

Shear yield: Used for cutting calculations in combat; higher is better. This is the raw value divided by 103 (i.e., kPa).

Shear fracture: Used for cutting calculations in combat; higher is better. This is the raw value divided by 103 (i.e., kPa).

Shear elasticity: Used for cutting calculations in combat; lower is better. This is the raw value.

General Term Explanations (From Wikipedia)

Yield Strength - The stress at which material strain changes from elastic deformation to plastic deformation, causing it to deform permanently.

Fracture Strength - The stress coordinate on the stress-strain curve at the point of rupture.

Stress - Force per area = F/A

Strain - Deformation of a solid due to stress = Stress/Young's Modulus

So...

Explanations!

Yield Strength is the amount of stress required to permanently deform (bend) a material (plastic deformation)

Fracture Strength is the amount of stress required to permanently break (rupture) a material

Elasticity (or IMPACT_STRAIN_AT_YIELD in RAWs) is the amount of deformation (bending) that occurs at the yield point

Implications to Dwarf Fortress Combat

Yield combined with Elasticity can tell what a material will do under stress (be it from a hammer, axe, or arrow)

Higher yield means that it takes more stress to deform

Lower elasticity means that it will deform less when stress is applied

Preliminary Combat Testing & Analysis

Adamantine and Steel take first and second place respectively, with Iron the third best material in the game. Beyond which, bronze is in a close tie with copper as to being the second worst material. As in older versions, silver continues to hold steady as the worst material available (no longer beneficial with wooden training weapons being available now) in regards to edged weaponry.
Additionally, with regards to blunt weapons all of the standard materials perform respectably well, with a very slight edge towards steel and silver. Here is the thread with the details:

Keep in mind with how unbelievably complicated this system is nothing should be taken as word of law yet.

Best

Better

Good

Fair

Poor

Terrible

Notes

Armor

Adamantine

Steel

Iron

Bronze, Bismuth Bronze

Copper

Edged Weapons

Adamantine

Steel

Iron

Bronze, Bismuth Bronze

Copper

Silver

For piercing iron armor, copper is better than bronze. For piercing copper or bronze armor, bronze is better than copper.

Ammunition

Steel, Iron, Bronze, Bismuth Bronze, Copper, Silver

Adamantine

Adamantine bolts deflect off of adamantine armor, but otherwise their performance is on par with bolts made out of other metals.

Blunt Weapons

Platinum

Steel, Silver

Copper, Bismuth Bronze, Bronze, Iron

Adamantine

All six standard weapon metals perform nearly identically. Steel has a slightly higher rate of critical wounds, while silver is slightly more likely to penetrate armor. Platinum (only available as artifact weapons) has twice the density of silver and several other improved properties, making it the best metal for impact weapons, though very limited in production.

Cross referencing this table with the table at the top of this section seems to indicate that low densities, high impact fractures, and high shear fractures contribute to the killing power of edged weapons